with a clear presence of space derivatives unlike the lower gamma case. One can compare this action with the \(2d\)  worldsheet actions found in relation to Inhomogeneous super-BMS symmetries for tensionless strings in [1]}, [2]} and see this is a natural higher dimensional analogue of the one written there. Now we can easily find out the equations of motion:
\(\dot{\phi }=0,\quad \dot{\chi } = \sigma ^i\partial _i\phi .\) 
